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Josephus' Antiquities are one of the most famous sources outside the Bible from the first century AD on John the Baptist, Jesus, and his brother James. Many scholars consider Josephus' passage about Jesus (the "Testimonium Flavianum") to be either an interpolation or to have been reworked by Christians into a pro-Christian passage, although I think that it is probably authentic. However, the Antiquities are also important as one of the main ancient sources, outside the Bible and outside rabbinical traditions, about the Biblical period and the ancient Jewish history that followed it.

(Question 1) What does OPISTHOGRAPHA mean, and how would you translate the underlined part that M. Weill renders "deux et demie par colonne"?
In Book 3 of the Antiquities, Josephus records details about the throne of God having Cherubim, and about the tablets of the 10 Commandments, details that are not in the Bible:

To the cover were affixed two figures, (Ex. xxv.) " cherubs " as the Hebrews call them—winged creatures these, but in form unlike to any that man's eyes have seen, and Moses says that he saw them sculptured upon the throne of God.(Footnote A) Within this ark he deposited the two tables, whereon had been recorded the ten commandments, five on each of them, and two and a half on either face.(FOOTNOTE B) The ark itself he laid up in the sanctuary.

Thackeray's footnotes
(A) Not in the Pentateuch, nor apparently (to judge from M. Weill's silence) in any known Rabbinical tradition. Perhaps,
as suggested by M. Weill, a reminiscence of Ezekiel's vision, in which cherubim uphold the firmament which supports God's throne (Ezek. x. 1).
(B) The tables being regarded as OPISTHOGRAPHA. For this last detail no parallel has been found in Rabbinical tradition for "five on each" cf. § 101 note. M. Weill, however, renders "deux et demie par colonne."

(Question 2) Does Josephus say that Aristobulus was "kindly" or had "candor"?
According to Loeb's translation of Book XIII of the Antiquities, Josephus says of John Hyrcanus' son, King Aristobulus:

Now of his brothers he loved only Antigonus, who was next in age, and considered him worthy of a position like his own, while he kept his other brothers in chains. He also imprisoned his mother, who had disputed the royal power with him—for Hyrcanus had left her mistress of the realm—, and carried his cruelty so far that he caused her to die of starvation in prison...

He [ie. Aristobulus] had a kindly nature, and was wholly given to modesty, as Strabo also testifies on the authority of Timagenes,* writing as follows. " This man was a kindly person and very serviceable to the Jews,

Whiston translates the part in question as, "He was naturally a man of candor, and of great modesty, as Strabo bears witness, in the name of Timagenes; who says thus: 'This man was a person of candor, and very serviceable to the Jews;'"

"Gaius Caesar, our consular praetor, by edict forbade religious societies to assemble in the city, but these people [the Jewish inhabitants of the city] alone he did not forbid to do so or to collect contributions of money or to hold common meals. Similarly do I forbid other religious societies but permit these people alone to assemble and feast in accordance with their native customs and ordinances."

It sounds like a very strict edict that could impact Christians as well as other religious groups. It's curious - would even mainstream Roman pagan groups be affected?

Whiston's translation makes the ban more limited:

for even Caius Caesar, our imperator and consul, in that decree wherein he forbade the Bacchanal rioters to meet in the city, did yet permit these Jews, and these only, both to bring in their contributions, and to make their common suppers. Accordingly, when I forbid other Bacchanal rioters, I permit these Jews to gather themselves together, according to the customs and laws of their forefathers, and to persist therein. It will be therefore good for you, that if you have made any decree against these our friends and confederates, to abrogate the same, by reason of their virtue and kind disposition towards us.

(Question 4) In Book XVI of Josephus' Antiquities, did Herod's two young sons complain that they were forced "to share the same fate" as their mother, or did they complain that they were forced to be partakers with those who killed her?
The Greek text says:

In Loeb's edition, Ralph Marcus translates it as saying that the youths were forced "to share the same fate" as their mother.

Here is Whiston's translation of the full section, with the statement in question coming at the end:

1. BUT now the affairs in Herod's family were in more and more disorder, and became more severe upon him, by the hatred of Salome to the young men [Alexander and Aristobulus], which descended as it were by inheritance [from their mother Mariamne]; and as she had fully succeeded against their mother, so she proceeded to that degree of madness and insolence, as to endeavor that none of her posterity might be left alive, who might have it in their power to revenge her death. The young men had also somewhat of a bold and uneasy disposition towards their father occasioned by the remembrance of what their mother had unjustly suffered, and by their own affectation of dominion. The old grudge was also renewed; and they east reproaches on Salome and Pheroras, who requited the young men with malicious designs, and actually laid treacherous snares for them. Now as for this hatred, it was equal on both sides, but the manner of exerting that hatred was different; for as for the young men, they were rash, reproaching and affronting the others openly, and were inexperienced enough to think it the most generous to declare their minds in that undaunted manner; but the others did not take that method, but made use of calumnies after a subtle and a spiteful manner, still provoking the young men, and imagining that their boldness might in time turn to the offering violence to their father; for inasmuch as they were not ashamed of the pretended crimes of their mother, nor thought she suffered justly, these supposed that might at length exceed all bounds, and induce them to think they ought to be avenged on their father, though it were by despatching him with their own hands. At length it came to this, that the whole city was full of their discourses, and, as is usual in such contests, the unskilfulness of the young men was pitied; but the contrivance of Salome was too hard for them, and what imputations she laid upon them came to be believed, by means of their own conduct; for they who were so deeply affected with the death of their mother, that while they said both she and themselves were in a miserable case, they vehemently complained of her pitiable end, which indeed was truly such, and said that they were themselves in a pitiable case also, because they were forced to live with those that had been her murderers, and to be partakers with them.

(Question 1) What does OPISTHOGRAPHA mean, and how would you translate the underlined part that M. Weill renders "deux et demie par colonne"?

Just a word of advice -- you write too much in one post, and that makes answering your multiple questions rather daunting. I would suggest breaking it up into several posts -- that way people might feel better about answering. As for your question above:

noun
a manuscript, parchment, or book having writing on both sides of the leaves.

The author cited above uses it with a Greek neuter plural for the plural, parallel to terms like autographa (used in some scholarly circles as the plural of autograph, not a signature, but the first manuscript written or dictated by an ancient author from which all subsequent copies descend).

This says that the ten commandments were split between the two slabs, five on each (ἀνὰ πέντε μὲν εἰς ἑκατέραν), two and a half commandments per column (ἀνὰ δύο δὲ καὶ ἥμισυ κατὰ μέτωπον—implying that each slab had two columns). In such context μέτωπον refers to the written area bordered by the surrounding margins. It's wrong to imagine that the tablets were opisthographs.

Looking through all of Josephus' uses of μέτωπον, which he uses to mean geometric "face" or "front" a great number of times -- unlike the Septuagint or NT, which do not ever use it that way -- I can't convince myself that he means "columns." There's nothing comparable that I could find.

But an opisthograph would seem strange too. Could he mean two and a half spans to a face? Ie., given the dimensions for the ark a sentence earlier, they'll lay side-by-side.

Looking through all of Josephus' uses of μέτωπον, which he uses to mean geometric "face" or "front" a great number of times -- unlike the Septuagint or NT, which do not ever use it that way -- I can't convince myself that he means "columns." There's nothing comparable that I could find.

But an opisthograph would seem strange too. Could he mean two and a half spans to a face? Ie., given the dimensions for the ark a sentence earlier, they'll lay side-by-side.

The idea of "face" or "side" of the tablet seems to make the most sense to me as well.

Why would an opisthograph be strange? It is a common theme in biblical literature, both in Hebrew (note Ezekiel) and in Greek (note the book of Revelation). Not saying that has to be the meaning here, but it does not strike me as odd that it would be described that way, except for the fact that half a commandment would end up being written on one side and the other half on the other.